Trajectory tracking and consensus of networks of Euler–Lagrange systems

Abstract

This paper addresses the problem of synchronizing networks of nonidentical, nonlinear dynamical systems described by Euler–Lagrange equations. It is assumed that the communication graph is simply connected and that the systems are fully actuated, with their states available for measurement. The communications can be subject to constant time-delays. The main result of the paper is a controller for each system in the network, capable of tracking a desired trajectory and, if such trajectory does not exist, capable of reaching a network consensus. Moreover, it is proved that, if there are no time-delays and the graph is balanced each system reaches a consensus arbitrarily near the average of the initial conditions of all the systems in the network. Simulations using a ten robot manipulator network with different time-delays are provided.